Refraction statics for complex near-surface models

Abstract

Most of the conventional methods for the computation of refraction static corrections assume a linear decomposition of the travel-times according to a model that is actually appropriate only for the description of very regular near-surface structures. Complex structures of the upper layers are inaccurately solved by these methods. In earlier work of the author, the analytical discussion of the model-accuracy led to error-predicting equations. Thus, the solution-accuracy can be considerably improved by upgrading the linear model with the error-predicting equations. Alternatively, it is also possible to improve the accuracy by applying linear operators which generalize the particular solution in order to derive the more robust functions of the Generalized Reciprocal Method. The near-surface structure is sometimes complicated by gradual variations in velocity with depth, or by the rapid succession of thin layers. As a result, the travel-time curves may deviate far from the straight line which is expected from the linear decomposition scheme. The natural extension of the method to deal with hard variations of the velocity, i.e. discontinuities in the slope of the travel-time curve, is the successive inversion of curve segments of constant slope. For the soft variations of the velocity field, a first approximation of the travel-time reduction vs. offset was derived; the effect can be efficiently modeled provided a new parameter is included in the model equation. A further improvement to the robustness of the solution is easy to achieve if the data inversion is performed in the wavenumner-offset domain. This domain is the most convenient both for reducing the computation time and for implementing an efficient routine which automatically removes the mispicks. Real data experiments validate the theory presented in this paper and show encouraging results in terms of good quality stacks.